You'll do fine with just the seven Civil War titles. You might miss a few things that happens alongside, but the main points will get across. You might want to check out eleven-issue Civil War: Frontlines, which tells the tales of two journalists, and Speedball.

Personally, I find that the the more you read the more interesting the arc becomes. But if you don't want to read everything I recommend that you read (Apart from Civil War and Civil war: Frontlines) Iron Man's, Spider-Man's and Captain America's respective runs. The exact issues can be found on the Wikipedia-page for the Civil War.

Thanks. Front Line sounds interesting; I loved Marvels because of the journalism aspect. I may check out some of the related runs but the list is massive so I wanted to see what people thought were more dire and which could be tossed aside.

I believe the ones I listed are the most dire ones — there are some pretty intense scenes between Iron Man and Spidey. Fantastic Four might be worth a read as well, because of... Well, you'll see it if you read it. I don't really enjoy the Fantastic Four, but the Civil War-tie ins are pretty moving.

There's a marvel tpb that's called Civil War: The Road to Civil War, it collects a few FF and Spider-Man issues as well as a Illuminati one shot. As you can probably guess it directly leads into the Civil War story. I would definitely recommend that.